Gebel and colleagues1 reported a seemingly simple and accurate method for estimating the volume of a subdural hematoma. However, as 17th century philosopher and mathematician Thomas Hobbes wrote about a similarly bewildering calculation, “To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad.”2

The ABC/2 method for an intraparenchymal hematoma is based on the formula for the volume of a ellipsoid which is given by 4/3 π r1r2r3 (where the r represents each radius). With an approximation of 3 for π, and substitution of each of the radii with each diameter (d) divided by 2, the formula becomes d1d2d3/2, or ABC/2.

At first, it seems quite unlikely that this formula should be useful in the estimation of the volume of a crescent-shaped subdural hematoma. Nevertheless, the method has proven accuracy, and its derivation must be explained. Consider the 3-dimensional crescent as the difference between 1 large outer ellipsoid and 1 small inner ellipsoid, which is then cut in half (ie, the crescent is akin to a solid semicircle). The volume of the crescent is then given by (4/3 π r1r2r3 −4/3 π r4r5r6)/2. Using the measurements as defined by Gebel et al1 (Figure⇓ ), the length (L) represents 1 diameter, the thickness (T) represents another, and these are the same for both the inner and outer ellipsoids. The width (w) of the 2 ellipsoids differs, so the formula can then be approximated as (LTw2−LTw1)/2. Since the difference between the widths is represented by W, the entire formula simplifies to LTW/2, or ABC/2.

Thus, “Though this be madness, yet there is method in ’t.”3 Was this the method of Gebel et al?

Volume of a subdural hematoma (gray area) can be approximated by halving the difference in volume between a large outer ellipsoid (solid line) and a small inner ellipsoid (dashed line). Two of the 3 diameters of both ellipsoids are identical: the length (L), and the thickness (T) which is perpendicular to the plane shown. The third radius is designated as the width (w), and the difference between the widths of the 2 ellipsoids is marked by W.